[asddkk]

I think there's some information-theoretic ideas about compressibility or codelength that are relevant.

The appeal, I think, is in being able to succinctly represent a random or irrational mathematical object with some other object that's not exactly the same, but is simpler to describe and equivalent to some high degree of similarity. Normally these ideas are applied to things that are thought of as random in a physically stochastic sense, but you could apply them to things that are random in an information-theoretic irrationality sense also.

I'd say the polyhedra they discuss are kind of examples of this, maybe in reverse or something: they are simplified constructs that work as representations to some close extent.

There's some interesting ties here to pseudorandom numbers, in that usually we think of them as approximating true randomness, even though they're entirely reproducible and predictable. This seems similar to me at some level.